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arXiv · 1902.05253

High-order generalized-$\alpha$ methods

Quanling Deng·Pouria Behnoudfar·Victor M. Calo
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Abstract

The generalized-$\alpha$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user. The method is unconditionally stable and is of second-order accuracy in time. We extend the second-order generalized-$\alpha$ method to third-order in time while the numerical dissipation can be controlled in a similar fashion. We establish that the third-order method is unconditionally stable. We discuss a possible path to the generalization to higher order schemes. All these high-order schemes can be easily implemented into programs that already contain the second-order generalized-$\alpha$ method.

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Quanling Deng, Pouria Behnoudfar, Victor M. Calo. 2019-02-14. High-order generalized-$\alpha$ methods. https://arxiv.org/abs/1902.05253

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